Real numbers having ultimately periodic representations in abstract numeration systems
Computational Complexity
2007-05-23 v1 Computation and Language
Abstract
Using a genealogically ordered infinite regular language, we know how to represent an interval of R. Numbers having an ultimately periodic representation play a special role in classical numeration systems. The aim of this paper is to characterize the numbers having an ultimately periodic representation in generalized systems built on a regular language. The syntactical properties of these words are also investigated. Finally, we show the equivalence of the classical "theta"-expansions with our generalized representations in some special case related to a Pisot number "theta".
Keywords
Cite
@article{arxiv.cs/0212018,
title = {Real numbers having ultimately periodic representations in abstract numeration systems},
author = {P. Lecomte and M. Rigo},
journal= {arXiv preprint arXiv:cs/0212018},
year = {2007}
}
Comments
22 pages, 10 figures